Factor the following expression: $81x^2 - 1$
Solution: The expression is of the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b}) ({a} - {b})$ What are the values of $a$ and $b$ $ a = \sqrt{81x^2} = 9x$ $ b = \sqrt{1} = 1$ Use the values we found for $a$ and $b$ to complete the factored expression, $({a} + {b}) ({a} - {b})$ So we can factor the expression as: $({9x} + {1}) ({9x} - {1})$